The first 9 instructions (TITL...UNIT) are the same for any SHELXS and SHELXL-93 job for this structure and define the cell dimensions, symmetry and contents. The Siemens SHELXTL program XPREP can be used to generate these instructions automatically for any space group etc. SHELXL-93 knows the scattering factors for the first 94 neutral atoms in the Periodic Table. Ten least-squares cycles are to be performed, and the ACTA instruction ensures that the CIF files 'ags4.cif' and 'ags4.fcf' will be written for archiving and publication purposes. ACTA also sets up the calculation of bond lengths and angles (BOND) and a final difference electron density synthesis (FMAP 2) with peak search (PLAN 20). The HKLF 4 instruction terminates the file and initiates the reading of the 'ags4.hkl' intensity data file.
Users migrating from SHELX-76 should note that it is still legal to set up special position constraints on the x,y,z-coordinates, occupation factors, and Uij components (for upwards compatibility). However it is totally unnecessary because the program will do this automatically for any special position in any space group, conventional or otherwise. Similarly the program recognizes polar space groups (P-4 is non-polar) and applies appropriate restraints (H.D. Flack and D. Schwarzenbach, Acta Cryst., A44 (1988) 499-506), so it is no longer necessary to worry about fixing one or more coordinates to prevent the structure drifting along polar axes. It is not necessary to set the overall scale factor using an FVAR instruction for this initial job, because the program will itself estimate a suitable starting value. Comments may be included in the '.ins' file either as REM instructions or as the rest of a line following '!'; this latter facility has been used to annotate this example.
TITL AGS4 in P-4 ! title of up to 76 characters CELL 0.71073 8.381 8.381 6.661 90 90 90 ! wavelength and unit-cell ZERR 1 .002 .002 .001 0 0 0 ! Z (formula-units/cell), cell esd's LATT -1 ! non-centrosymmetric primitive lattice SYMM -X, -Y, Z SYMM Y, -X, -Z ! symmetry operators (x,y,z must be left out) SYMM -Y, X, -Z SFAC C AG AS F N S ! define scattering factor numbers UNIT 4 1 1 6 4 8 ! unit cell contents in same order L.S. 10 ! 10 cycles full-matrix least-squares ACTA ! CIF-output, bonds, Fourier, peak search OMIT -2 3 1 ! suppress bad reflection ANIS ! convert all (non-H) atoms to anisotropic WGHT 0.037 0.31 ! weighting scheme AG 2 .000 .000 .000 AS 3 .500 .500 .000 S1 6 .368 .206 .517 ! atom name, SFAC number, x, y, z (usually S2 6 .614 .966 .736 ! followed by sof and U(iso) or Uij); the C 1 .278 .095 .337 ! program automatically generates special N 5 .211 .030 .214 ! position constraints F1 4 .596 .325 -.007 F2 4 .500 .500 .246 HKLF 4 ! read h,k,l,Fo2,sigma(Fo2) from 'ags4.hkl'
Covalent radii and connectivity table for AGS4 in P-4 C 0.770 AG 1.440 AS 1.210 F 0.640 N 0.700 S 1.030 Ag - N N_$4 N_$5 N_$3 As - F2 F2_$6 F1_$7 F1_$6 F1_$1 F1 S1 - C S2_$1 S2 - S2_$2 S1_$1 C - N S1 N - C Ag F1 - As F2 - As Operators for generating equivalent atoms: $1 -x+1, -y+1, z $2 -x+1, -y+2, z $3 -x, -y, z $4 y, -x, -z $5 -y, x, -z $6 y, -x+1, -z $7 -y+1, x, -z
EQIV $1 1-x, 1-y, z EQIV $2 x, y-1, z EQIV $3 1-x, -y, z CONF S1 S2_$1 S2_$2 S1_$3could have been included in 'ags4.ins' to calculate the S-S-S-S torsion angle. Only one new operator would have been required if S2 were bonded to S1 in the original atom list. If EQIV instructions are used, the program renumbers the other symmetry operators accordingly.
The next part of the output is concerned with the data reduction:
1475 Reflections read, of which 0 rejected
0 =< h =< 10, -9 =< k =< 10, 0 =< l =< 8, Max. 2-theta = 55.00
0 Systematic absence violations
Inconsistent equivalents etc.
h k l Fo^2 Sigma(Fo^2) Esd of mean(Fo^2)
3 4 0 387.25 8.54 47.78
1 Inconsistent equivalents
904 Unique reflections, of which 1 suppressed
R(int) = 0.0165 R(sigma) = 0.0202 Friedel opposites not merged
Maximum memory for data reduction = 955 / 9083
R(int) = Sigma | Fo2 - Fo2(mean) | / Sigma [ Fo2 ]
where both summations involve all input reflections for which more than one symmetry equivalent is averaged, but not the remaining reflections, and:
R(sigma) = Sigma [ sigma(Fo2) ] / Sigma [ Fo2 ]
over all reflections in the merged list. Since these R-indices are based on F2, they will tend to be about twice as large as the corresponding indices based on F. The 'esd of the mean' (in the table of inconsistent equivalents) is the rms deviation from the mean divided by the square root of (n-1), where n equivalents are combined for a given reflection. In estimating the sigma(F2) of a merged reflection, the program uses the value obtained by combining the sigma(F2) values of the individual contributors, unless the esd of the mean is larger, in which case it is used instead.
The memory statistics which appear at various points in the output give the highest elements of the A and B arrays used for the given calculation. Although it is easy to adjust these dimensions, it requires recompiling the program and will rarely be required. For example there is no limit on the number of reflections in this sort/merge stage - if there is less physical memory the program makes more use of the disk, which of course is slower.
Special position constraints are then generated and the statistics from the first least-squares cycle are listed (the output has been compacted to fit the page). The maximum vector length refers to the number of reflections processed simultaneously in the rate-determining calculations; usually the program utilizes all available memory to make this as large as possible, subject to a maximum of 511. This maximum may be reduced (but not increased) by means of the fourth parameter on the L.S. (or CGLS) instruction; this may be required to prevent unnecessary disk transfers when large structures are refined on virtual memory systems with limited physical memory. The number of parameters refined in the current cycle is followed by the total number of refinable parameters (here both are 55).
Special position constraints for Ag
x = 0.0000 y = 0.0000 z = 0.0000 U22 = 1.0 * U11
U23 = 0 U13 = 0 U12 = 0 sof = 0.25000
Special position constraints for As
x = 0.5000 y = 0.5000 z = 0.0000 U22 = 1.0 * U11
U23 = 0 U13 = 0 U12 = 0 sof = 0.25000
Special position constraints for F2
x = 0.5000 y = 0.5000 U23 = 0 U13 = 0
sof = 0.50000
Least-squares cycle 1 Maximum vector length =511 Memory required =1095/82388
wR2 = 0.5042 before cycle 1 for 903 data and 55 / 55 parameters
GooF = S = 3.480; Restrained GooF = 3.480 for 0 restraints
Weight = 1/[sigma^2(Fo^2)+(0.0370*P)^2+0.31*P] where P=(Max(Fo^2,0)+2*Fc^2)/3
** Shifts scaled down to reduce maximum shift/esd from 17.32 to 15.00 **
N value esd shift/esd parameter
1 2.38015 0.04260 32.401 OSF
2 0.08362 0.00224 14.993 U11 Ag
5 0.02864 0.00580 -3.679 U33 As
11 0.08546 0.00781 4.543 U33 S1
23 -0.01788 0.00444 -4.027 U12 S2
47 0.14422 0.01515 6.218 U33 F1
52 0.13288 0.02330 3.558 U11 F2
Mean shift/esd = 2.053 Maximum = 32.401 for OSF
Max. shift = 0.055 A for C Max. dU = 0.049 for F2
Final Structure Factor Calculation for AGS4 in P-4 Total number of l.s. parameters = 55 Maximum vector length = 511 wR2 = 0.0779 before cycle 11 for 903 data and 2 / 55 parameters GooF = S = 1.063; Restrained GooF = 1.063 for 0 restraints Weight = 1/[sigma^2(Fo^2)+(0.0370*P)^2+0.31*P] where P=(Max(Fo^2,0)+2*Fc^2)/3 R1 = 0.0322 for 818 Fo > 4.sigma(Fo) and 0.0370 for all 904 data wR2 = 0.0834, GooF = S = 1.138, Restrained GooF = 1.138 for all data Flack x parameter = 0.0224 with esd 0.0260 (expected values are 0 (within 3 esd's) for correct and +1 for inverted absolute structure)
Since the structure is non-centrosymmetric, the program has automatically estimated the Flack absolute structure parameter x in the final structure factor summation. In this example x is within one esd of zero, and its esd is also relatively small. This provides strong evidence that the absolute structure has been assigned correctly, so that no further action is required. The program would have printed a warning here if it would have been necessary to 'invert' the structure. For further details see the section on absolute structure below. The two parameters 'refined' ( 2 / 55 ) but not applied in the final structure factor cycle in this case are related to the overall scale and the Flack x parameter; no parameters are 'refined' in the final structure factor cycle for a centrosymmetric structure.
This is followed by a list of principal mean square displacements U for all anisotropic atoms. It will be seen that none of the smallest components (in the third column) are in danger of going negative [which would make the atom 'non positive definite' (NPD)] but that the motion of the two unique fluorine atoms is highly anisotropic (not unusual for an AsF6 anion). The program suggests that the fluorine motion is so extended in one direction that it would be possible to represent each of the two fluorine atoms as disordered over two sites, for which x, y and z coordinates are given; this may safely be ignored here (although there may well be some truth in it). The two suggested new positions for each 'split' atom are placed equidistant from the current position along the direction (and reverse direction) corresponding to the largest eigenvalue of the anisotropic displacement tensor.
This list is followed by the analysis of variance (reproduced here in squashed form), recommended weighting scheme (to give a flat analysis of variance in terms of Fc2), and a list of the most disagreeable reflections (which clearly shows that the one reflection suppressed by OMIT is indeed an aberration). For a discussion of the analysis of variance see the second example.
Principal mean square atomic displacements U
0.1067 0.1067 0.0561 Ag
0.0577 0.0577 0.0386 As
0.1038 0.0659 0.0440 S1
0.0986 0.0515 0.0391 S2
0.0779 0.0729 0.0391 C
0.1004 0.0852 0.0474 N
0.3029 0.0954 0.0473 F1
may be split into 0.5965 0.3173 0.0288 and 0.5946 0.3324 -0.0369
0.4778 0.1671 0.0457 F2
may be split into 0.5320 0.5089 0.2462 and 0.4680 0.4911 0.2462
Analysis of variance for reflections employed in refinement
K = Mean[Fo^2] / Mean[Fc^2] for group
Fc/Fc(max) 0.000 0.026 0.039 0.051 0.063 0.082 0.103 0.147 0.202 0.306 1.0
Number in group 94. 89. 90. 91. 89. 91. 89. 91. 88. 91.
GooF 1.096 1.101 0.997 1.078 1.187 1.069 1.173 0.922 1.019 0.966
K 1.560 1.053 1.010 1.004 1.007 1.021 1.026 1.002 0.997 0.984
Resolution(A) 0.77 0.81 0.85 0.90 0.95 1.02 1.10 1.22 1.40 1.74 inf
Number in group 97. 84. 92. 91. 89. 90. 89. 90. 93. 88.
GooF 1.067 0.959 0.935 0.895 1.035 1.040 1.115 1.149 1.161 1.228
K 1.047 1.010 1.009 0.991 1.004 0.996 0.989 1.012 0.997 0.982
R1 0.166 0.100 0.069 0.059 0.051 0.036 0.033 0.027 0.020 0.020
Recommended weighting scheme: WGHT 0.0329 0.3591
Most Disagreeable Reflections (* if suppressed)
h k l Fo^2 Fc^2 Delta(F^2)/esd Fc/Fc(max) Resolution(A)
* -2 3 1 43.53 7.44 11.14 0.029 2.19
4 4 4 18.32 33.30 3.51 0.062 1.11
-4 1 3 15.79 4.17 3.39 0.022 1.50
0 2 2 41.60 57.32 3.16 0.082 2.61
2 5 0 124.72 100.33 3.06 0.108 1.56
2 3 0 64.43 48.46 3.03 0.075 2.32
-5 4 1 11.04 2.57 2.90 0.017 1.28
2 5 3 42.27 55.48 2.60 0.080 1.27
6 5 2 6.43 1.02 2.56 0.011 1.02
4 6 2 20.16 11.98 2.55 0.037 1.10
6 1 1 55.45 42.28 2.51 0.070 1.35
6 0 5 104.65 126.19 2.49 0.121 0.96
4 1 2 139.30 116.95 2.44 0.117 1.74
9 0 3 39.34 26.06 2.44 0.055 0.86
2 4 4 371.53 327.01 2.36 0.195 1.24
4 3 5 55.69 43.02 2.33 0.071 1.04
-3 6 0 7.51 3.10 2.25 0.019 1.25
-1 4 2 142.05 120.53 2.22 0.119 1.74
0 10 1 2.01 8.31 2.21 0.031 0.83
-2 1 2 1497.02 1361.86 2.20 0.399 2.49
The algorithm for generating the 'asymmetric unit' for the Fourier calculations is general for all space groups, in conventional settings or otherwise. The rms electron density (averaged over all grid points) is printed as well as the maximum and minimum values so that the significance of the latter can be assessed. Since PLAN 20 was assumed, only a peak list is printed (and written to the .res file), followed by a list of shortest distances between peaks (not shown below); PLAN -20 would have produced a more detailed analysis with 'printer plots' of the structure. The last 40 peaks and some of the interatomic distances have been deleted here to save space. In this table, 'distances to nearest atoms' takes symmetry equivalents into account.
Bond lengths and angles [severely squashed to fit 80 columns!]
Ag - Distance Angles
N 2.279(0.006)
N_$4 2.279(0.006) 113.08(0.15)
N_$5 2.279(0.006) 113.08(0.15) 102.47(0.29)
N_$3 2.279(0.006) 102.47(0.29) 113.08(0.16) 113.08(0.15)
Ag - N N_$4 N_$5
As - Distance Angles
F2 1.640(0.007)
F2_$6 1.640(0.007)180.00(0.00)
F1_$7 1.672(0.004) 89.08(0.41) 90.92(0.41)
F1_$6 1.672(0.004) 89.08(0.41) 90.92(0.41)178.18(0.82)
F1_$1 1.672(0.004) 90.92(0.41) 89.08(0.41) 90.01(0.01) 90.01(0.01)
F1 1.672(0.004) 90.92(0.41) 89.08(0.41) 90.01(0.01) 90.01(0.01)178.18(0.82)
As - F2 F2_$6 F1_$7 F1_$6 F1_$1
S1 - Distance Angles
C 1.682(0.007)
S2_$1 2.063(0.003) 98.61(0.20)
S1 - C
S2 - Distance Angles
S2_$2 2.011(0.003)
S1_$1 2.063(0.003) 105.37(0.07)
S2 - S2_$2
C - Distance Angles
N 1.147(0.007)
S1 1.682(0.007) 175.67(0.49)
C - N
N - Distance Angles
C 1.147(0.007)
Ag 2.279(0.006) 152.38(0.45)
N - C
F1 - Distance Angles
As 1.672(0.004)
F1 -
F2 - Distance Angles
As 1.640(0.007)
F2 -
FMAP and GRID set by program
FMAP 2 3 18
GRID -3.333 -2 -1 3.333 2 1
R1 = 0.0370 for 590 unique reflections after merging for Fourier
Highest memory used 768 / 6109
Electron density synthesis with coefficients Fo-Fc
Maximum = 0.32, Minimum = -0.35 e/A^3, Highest memory used = 768/13827
Mean = 0.00, Rms deviation from mean = 0.07 e/A^3
Fourier peaks appended to .res file
x y z sof U Peak Dist to nearest atoms
Q1 1 0.0000 0.0000 0.5000 0.25000 0.05 0.32 2.60 N 2.69 C 3.33 AG
Q2 1 0.5691 0.3728 0.1623 1.00000 0.05 0.27 1.20 F1 1.34 F2 1.62 AS
Q3 1 0.5685 0.3851 -0.1621 1.00000 0.05 0.24 1.19 F1 1.25 F2 1.56 AS
Q4 1 0.4075 0.4717 0.2378 1.00000 0.05 0.23 0.81 F2 1.78 AS 1.79 F1
Q5 1 0.5848 0.2667 0.0312 1.00000 0.05 0.23 0.55 F1 2.09 AS 2.47 F1
Q6 1 0.5495 0.3425 -0.1122 1.00000 0.05 0.21 0.83 F1 1.57 AS 1.65 F2
Q7 1 0.2617 -0.1441 0.1446 1.00000 0.05 0.20 1.59 N 2.17 F1 2.40 C
Q8 1 0.7221 0.1898 0.0030 1.00000 0.05 0.20 1.55 F1 2.39 N 2.54 N
Q9 1 0.1997 0.0293 0.1024 1.00000 0.05 0.19 0.75 N 1.79 C 1.82 AG
Q10 1 0.5394 1.0113 0.8165 1.00000 0.05 0.19 0.91 S2 1.41 S2 2.82 S1
Ahead to The '.hkl' Reflection Data File
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